I've seen these bands on many h.264 exports. The funky thing is you don't really see them if you're squarely in front of your LCD, they only appear if you look off-axis, which explains why you see them so readily on your laptop. The image you posted looks fine on my monitor, but if I turn it 45 degrees off axis the bands appear.
I've personally only seen this issue with h.264, in either an .m4v or .mov container, when exporting in a resolution smaller than the source through compressor. And not on all of them. I admit I never really looked too hard for a solution, as we use that codec mainly for client approvals. The clients that did see the bands were comforted with an export in another codec or a full-res screen grab, where they disappeared.
So I don't have a solution for you, but it's not a hardware issue with your laptop.
Jean Christophe wrote: "I've personally only seen this issue with h.264, in either an .m4v or .mov container, when exporting in a resolution smaller than the source through compressor. And not on all of them."
That seems to be exactly what's happening here. Normally I export a full size Quick Time from Final Cut, then drop that into Compressor to create the .m4v. THIS time, I exported from FCP into Compressor to create the .m4v. It took forever and a day, (probably creating all the green bands.) It also added some orange discoloration to some scenes. NONE of this shows on my normal monitors, only on the laptop.
Solution = Abandon Compressor for this type of work flow - . Export an Mpeg 4 from MPEG Stream Clip.